We develop a fully polynomial-time approximation scheme (FPTAS) for minimizing the weighted total tardiness on a single machine, provided that all due dates are equal. The FPTAS is obtained by converting an especially designed pseudopolynomial dynamic programming algorithm.
Kellerer, H., & Strusevich, V. A. (2006). A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date. Theoretical Computer Science, 369(1–3), 230–238. https://doi.org/10.1016/j.tcs.2006.08.030